Three-on-three basketball, which is coming to the Olympics in 2020, would seem to be a sport the United States could do well in. A team of, say, LeBron James, Stephen Curry and Anthony Davis would be unstoppable.

But should you take a look at the field for the three-on-three World Cup next month in the Philippines, you will see something curious. Kyrgyzstan is in the men’s lineup, as are Estonia, Jordan and Mongolia. But the United States is not.

The reason is an unusual qualifying system designed to grow the sport all year long as much as find the best teams for the World Cup. That could also keep the United States, the birthplace of basketball and home to the world’s best players, out of the Olympics as well.

FIBA, the international basketball organization, has high hopes for three-on-three basketball, and wants to increase the format’s profile quickly.

“It will bring another audience to the sport of basketball,” said Julian Debove, a senior communications manager at FIBA. He meant younger viewers, but, just as important, FIBA sees three-on-three as a boon for smaller countries. “It’s a new opportunity for member organizations to participate and win medals,” Debove said. “To be successful in basketball, you need eight to 12 guys who can perform. In three-on-three, if you have four players with high-level talent you can win medals.”

Medal winners in the first four World Cups include Qatar and the Netherlands on the men’s side and Belgium, Hungary and Czech Republic for women, none of which are traditional basketball powers.

The field for the World Cup is based entirely on ranking: There was no qualifying tournament. And at the cutoff date last year, the United States men ranked 12th, behind Latvia and Estonia. The women were 13th behind Venezuela, Hungary and even Andorra.

One reason is that mere participation in three-on-three events can earn points. “Andorra has heavy participation every weekend,” Debove said.

Since many of the top-ranking events are in Europe, the opportunity for Americans to participate is smaller.

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France and Slovenia faced off in a semifinal match in the 2017 FIBA 3x3 World Cup.CreditLoic Venance/Agence France-Presse — Getty Images

Individual rankings are also factored in. So a James-Curry-Davis dream team would have no ranking points at all unless the stars took the unlikely route of hitting the European three-on-three circuit.

FIBA has created this system because it wants to promote its three-on-three tour, not just the Olympics and the World Cup. It also wants to establish players who are three-on-three stars, not borrowed from five-on-five basketball. “Where we want to go is professionals who play the whole season,” Debove said.

But that just isn’t likely for American players in the near future. “The reality in the short term is that we’ll have five-on-five players who will play three-on-three,” said Jim Tooley, chief executive of U.S.A. Basketball.

“It’s very important to U.S.A. Basketball,” Tooley said of the three-on-three game. “I love the idea that it gets the sport to parts of the world where otherwise it wouldn’t be.” So the United States is doing its best to adapt to the qualifying system.

“Tournaments are at challenging times for the players,” Tooley acknowledged. “We can start hosting some events here, to qualify for the Olympics. But the big events are not here. We can start a tournament and submit it tomorrow, but it would have very low points.”

In another boost for small nations, the 20 men’s and 20 women’s teams at the World Cup must come from 30 different countries. That makes it difficult for countries with strong teams of both genders, like the United States. For this World Cup, the American women are in, but the men are out.

FIBA is clearly trying to establish the sport, and maintain control of it. It takes pains, for example, to refer to it by its branded name, “3x3,” rather than “three-on-three.” And only official FIBA-endorsed 3x3 events count in the rankings, not events like the Big3, the league started in the United States by Ice Cube last summer, for example.

For now, only the women will be representing the Americans internationally. The winner of the American qualifying tournament is a team of undergraduates from the University of Oregon. Arike Ogunbowale, who was named most valuable player of the N.C.A.A. tournament, was on a team that lost in the semifinals.

No final decision has been made on how the 2020 Olympics qualifiers will be chosen, but placement will be at a premium: There will be only eight teams for each gender. FIBA said it would consider adding a qualifying tournament, Debove said.

And while bolstering the sports prospects of smaller countries is a laudable goal, FIBA is keenly aware that a basketball tournament without the United States is missing something. “A lot of teams want to beat the U.S.,” Debove said. “Beating the U.S. teams is an achievement.”

This year, Nigeria, Ukraine and Japan won’t get that chance.

A version of this article appears in print on , on Page B10 of the New York edition with the headline: U.S. Could Dominate 3-on-3 Hoops. If Only It Could Qualify.. Order Reprints | Today’s Paper | Subscribe